Discrete-event stochastic systems with copula correlated input processes

Abstract

In this article, we develop a new method based on copulas to model correlated inputs in discrete-event stochastic systems. We first define a type of correlated stochastic process, called Copula Correlated Processes (CCPs), which we then use to model correlated inputs for discrete-event stochastic systems. In general, it is very difficult to analyze discrete-event stochastic systems with correlated inputs. However, we show that discrete-event stochastic systems with CCPs can be discretized and approximated by discrete-event stochastic systems with discrete copula correlated processes, which are equivalent to discrete-event stochastic systems driven by Markov-modulated processes and are much easier to analyze. An illustrative queueing example is provided to demonstrate how our method works.

KEYWORDS:

• Discrete-event stochastic systems
• correlated processes
• Markov-modulated processes
• copulas

Additional information

Funding

This work is supported in part by the National Natural Science Foundation of China under Grants 71720107003, 72033003, 71571048, 71972019, 71601169, by the Fundamental Research Funds for the Central Universities under Grant 2020CDXYJG019, by Zhejiang Provincial Natural Science Foundation of China under Grant LY20G010012.

Notes on contributors

Lei Lei

Lei Lei received the BS degree in Mathematics from Sun Yat-sen University, China and the PhD degree in management science from Fudan University, China, in 2012 and 2018, respectively. She joined the School of Economics and Business Administration at Chongqing University, Chongqing, China, in December 2018. Her research interests include discrete-event stochastic systems, sensitivity analysis and simulation with applications towards supply chain management and financial engineering.

Jian-Qiang Hu

Jian-Qiang Hu is the Distinguished Professor of Fudan University and the Hongyi Professor of Management Science in School of Management, Fudan University. He received his BS degree in applied mathematics from Fudan University, China, and MS and PhD degrees in applied mathematics from Harvard University. His research interests include discrete-event stochastic systems, simulation, stochastic optimization, with applications in supply chain management, financial engineering, and healthcare. He has published over 100 research papers and is a co-author of the book, Conditional Monte Carlo: Gradient Estimation and Optimization Applications (Kluwer Academic Publishers, 1997). He won the Outstanding Simulation Publication Award from INFORMS Simulation Society twice (1998, 2019) and the Outstanding Research Award from Operations Research Society of China in 2020.

Chenbo Zhu

Chenbo Zhu is an Associate Professor at the School of Management, Zhejiang University of Technology, China. He received his BM and PhD degrees in management science from Fudan University, China. His research is focus on revenue management, inventory management, supply chain management, and simulation optimization. His research is published in journals such as IEEE Transactions on Automatic Control, INFORMS Journal on Computing, Omega, and Annals of Operations Research.